In my mind "get along" could mean a minimum of toleration. Rodney King famously said, “Can’t we all just get along?” during the 1992 race riots in LA. A parent might tell quarreling children, "you need to learn to get along."
In describing a good relationship, it could be used, but I think it might be interpreted as an intentional understatement; one hinting at a stronger positive relationship. Or ironically, hinting at problems.
"'How do you like your roommate?' He answered, 'We get along'."
A follow up question might be, "what do you mean?"
'Get on' sounds very informal. "They are getting on well" could definitely be used to describe a blossoming relationship, or a successful marriage.
Hope this helps. I think there is a chance there may be regional differences in the interpretation of these phrases.